The main goal you want to obtain from an RTOS is determinism, most other features are already available in most other non-RTOS operating systems.
The -OS part in RTOS means Operating System, simply put, and as all other operating systems, RTOSes provide the required infrastructure for managing processor resources so you work on a higher level when designing your application. For accessing those functionalities the OS provides an API. Using that API you can use semaphores, message queues, mutexes, etc.
An RTOS has one requirement to be an RTOS, it must be pre-emptive. This means that it must support task priorities so when a higher-priority task gets ready to run, one of possible task states, the scheduler must switch the current context to that task.
This operation has two implications, one is the requirement of one precise and dedicated timer, tick timer, and the other is that, during context switching, there is a considerable memory operations overhead. The current CPU status, or CPU's in case of multi-core SoCs, must be copied into the pre-empted task's context information and the new ready to run task's context must be restored in the CPU.
ARM processors already provide support for the System Timer, which is intended for a dedicated use as an OS tick timer. Not so long ago, the tick timer was required to be implemented with a regular, non-dedicated timer.
One optimization in cores designed for RTOSes with real-time capabilities is the ability to save/restore the CPU context state with minimum code, so it results in much less execution time than that in regular processors.
It is possible to implement an RTOS in nearly any processor, and there are some implementations targeted to resource constrained cores. You mainly need a timer with interrupt capacity and RAM. If the CPU is very fast you can run the OS tick at high rates, sub-millisecond in some real-time applications with DSPs, or at a lower rate like just 10~100 ticks per second for applications with low timing requirements in low end CPUs.